The New Relativity

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Abstract
The Page-Milne relativity theories are shown to imply the continuous group concept in connection with the conditions of equivalence and the one-dimensional problem is studied. Motional invariants are determined. A quadratic form left invariant under permissible motions is found. The expression determined is a proper one for the quadratics given in noninvariant form by Milne and Page. A tentative suggestion is made to extend the theory by making this quadratic form central for correlating observations and the consequences are studied. The form is invariant under a three parameter continuous group though one of the new groups introduced this way seems difficult to interpret physically. The Lorentz transformation is not necessarily part of the group and even when admitted it must be used with care. Nevertheless, another relation similar to that of the Lorentz transformation always exists between coordinate assignments made by two observers, moving in a permissible way, on the set of particles moving with constant velocity relative to one of them. This generalizes a result given by Page. A fairly extensive category of motions is taken up in some detail and the motional equations found.

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